4 comments:

(a)66 cubes. I counted 6 in the middle and each of the four legs I counted 15, so 15 x 4 + 6 = 66.(b)To find out how many cubes when it's 12 high, i saw that there was a pattern. Each leg was 11+10+9+8+7+6+5+4+3+2+1 = 66 So it's 66 x 4 +12 = 276.(c)To find the number of cubes n high, I looked for a pattern. I drew pictures(strategy) of towers 1 high, 2 high, 3 high, and so on. I made a table(strategy) of how many cubes comprised each tower and I looked for a pattern(strategy). I found the pattern was to multiply the height, n, by the sum of the height and the previous height, or n(n+(n-1))

(a)66 cubes. I just looked at the picture and counted the cubes. I didn't think about counting one leg of the tower and multiplying by four...good idea, thanks(b)To find out how many cubes when it's 12 high, I just drew a picture(strategy) of a tower 12 high and counted the cubes, I got 276.(c)To find the height n high, I tried to make the problem simpler (strategy) I drew pictures of towers 1,2,3,4,5,6 high and counted the cubes, I made an organized list(strategy) of the heights and total cubes, I was looking for a pattern(strategy) but I could not find the pattern.

(a) 66 cubes. I actually used sugar cubes to rebuild this tower and counted the number of cubes (Act out or use objects strategy)(b) I didn't have enough cubes so I built the center of the tower 12 high, then one leg of the tower using sugarcubes and multiplied the leg times 4, I got 276 cubes.(find a pattern, use objects strategy, make it simpler)(c) To find the height n high, I used my sugar cubes again. I found that if I took the cubes from a leg and stacked them on the opposing leg, I could create a rectangular wall. It made it easy to calculate the number of cubes by multiplying the height and the width. I made walls of varying heights and made a table of the heights. I found a pattern, and to calculate n high, it's n(n+(n-1))